Significant Figures Calculator
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A significant figures calculator shows which digits of a measurement carry real information and applies the sig fig rules when you calculate. For example, 0.0040500 has 5 significant figures: the leading zeros only place the decimal point, while the captive zero and the trailing zeros count. In a calculation, 4.56 × 1.4 = 6.384 is reported as 6.4, because 1.4 has only 2 significant figures.
Rounding to a place value instead (nearest ten, tenth or whole number)? Use the Rounding Calculator.
| Digits | Counts? | Rule |
|---|---|---|
| 0 0 0 | No | Leading zero: only shows where the decimal point is. |
| 4 | Yes | Non-zero digit: non-zero digits always count. |
| 0 | Yes | Captive zero: a zero between non-zero digits counts. |
| 5 | Yes | Non-zero digit: non-zero digits always count. |
| 0 0 | Yes | Trailing zero after the decimal point: it was measured, so it counts. |
Show steps
- Skip leading zerosThe first 3 zeros only place the decimal point, so they do not count.
- Start at the first non-zero digitCounting starts at the 4. Every non-zero digit counts.
- Captive zeros count1 zero sits between non-zero digits, so it counts.
- Trailing zeros with a decimal point countThe 2 trailing zeros count because the decimal point shows the value was measured to that place.
- Total0.0040500 has 5 significant figures. Its last significant digit is at decimal place 7.
Next: round it in the Round to sig figs tab, or use the scientific notation converter.
How to use the significant figures calculator
- Count sig figs: type the number exactly as it was measured, including trailing zeros and the decimal point. Each digit is colored, and a table names the rule behind it. Enter several numbers separated by semicolons to count a list.
- Round to sig figs: enter a number and how many significant figures you need (1 to 30). You get the rounded value, scientific notation, the deciding digit and a table of the same number rounded to 1 through 6 or more figures.
- Calculate: type a whole calculation such as (12.52 + 3.1) × 2.00. The calculator applies the right rule to each step, carries the unrounded value forward and rounds once at the end.
- Use the two options when your course needs them: whether trailing zeros in a whole number such as 1200 count, and whether an exact 5 rounds up or to the even digit.
Numbers can have up to 40 digits and an exponent from −300 to 300. Write powers of ten as 3.0e4 or 3.0 × 10^4, and put counted or defined numbers in square brackets, such as [2], so they do not limit the answer.
Rules for counting significant figures
- Non-zero digits always count: 4.56 has 3.
- Captive zeros, between non-zero digits, always count: 505 has 3.
- Leading zeros never count. They only show where the decimal point is: 0.0049 has 2.
- Trailing zeros count when the number has a decimal point: 45.0 has 3 and 1200. has 4.
- Trailing zeros in a whole number without a decimal point are ambiguous. By the usual convention 1200 has 2, but it could have 3 or 4 if those zeros were measured. Scientific notation removes the doubt: 1.20 × 10³ has exactly 3.
In scientific notation only the digits of the coefficient count, so 6.022 × 10²³ has 4 significant figures. The power of ten just moves the decimal point.
| Number | Significant figures | Why |
|---|---|---|
| 0.0040500 | 5 | 3 leading zeros do not count; 4, 0, 5, 0, 0 do |
| 1200 | 2 (ambiguous, up to 4) | trailing zeros with no decimal point |
| 1200. | 4 | the decimal point makes the zeros count |
| 100.020 | 6 | captive zeros plus a trailing zero after the point |
| 0.000100 | 3 | leading zeros skipped, trailing zeros kept |
| 6.022 × 10²³ | 4 | only the coefficient counts |
| 3.0 × 10⁴ | 2 | the zero after the point counts |
| 800 | 1 (ambiguous, up to 3) | placeholder zeros |
Significant figures in calculations
The rule depends on the operation. Addition and subtraction care about place value, so the answer stops at the least precise decimal place. Multiplication and division care about relative precision, so the answer keeps the fewest significant figures.
| Operation | Rule | Example |
|---|---|---|
| Add, subtract | fewest decimal places | 12.11 + 18.0 + 1.013 = 31.123 → 31.1 |
| Multiply, divide | fewest significant figures | 4.56 × 1.4 = 6.384 → 6.4 |
| Power, root | same sig figs as the base | √2.00 = 1.41421… → 1.41 |
| Logarithm | decimal places = sig figs of the number | log(2.5 × 10⁻⁴) = −3.602… → −3.60 |
| Antilog, 10^x or e^x | sig figs = decimal places of x | 10^3.20 = 1,584.9… → 1.6 × 10³ |
| Exact numbers | never limit the answer | [2] × π × 1.50 = 9.4247… → 9.42 |
Worked example: a mixed calculation
Find (12.52 + 3.1) × 2.00. First the sum: 12.52 + 3.1 = 15.62. The number 3.1 stops at tenths, so the sum is good to the tenths, 15.6, which is 3 significant figures. Keep 15.62 for the next step. Then 15.62 × 2.00 = 31.24. Both factors carry 3 significant figures, so the answer is 31.2.
Worked example: subtraction can wipe out figures
Find (25.0 − 24.8) ÷ 1.023. The difference 0.2 is good only to the tenths, so it has just 1 significant figure, even though 25.0 and 24.8 each had 3. Dividing, 0.2 ÷ 1.023 = 0.1955…, which is reported as 0.2. Nearly equal measurements lose precision when you subtract them.
Worked example: exact numbers
The circumference of a circle with radius 1.50 cm is C = 2πr. The 2 is part of the formula and π is a defined constant, so both are exact. Only 1.50 limits the answer: 2 × π × 1.50 = 9.4247… cm, reported as 9.42 cm. Counted quantities (12 eggs) and defined conversions (100 cm = 1 m) are exact too.
Round once, at the end
Keep at least one extra digit in intermediate steps and round only the final answer. Rounding at every step lets small errors build up. In 2.35 × 1.5 + 0.43, the product 3.525 is good to 2 significant figures (the tenths), and 3.525 + 0.43 = 3.955 rounds to 4.0. If you round the product to 3.5 first, you get 3.5 + 0.43 = 3.93, which rounds to 3.9, a different answer. The calculator shows the reported value after each step but carries the full value, and it warns you when rounding early would change the result.
Rounding to significant figures
- Find the first non-zero digit and count the number of figures you need from there.
- Look at the next digit. If it is 5 or more, round up; if it is 4 or less, leave the last kept digit alone.
- Replace dropped whole-number digits with zeros and drop decimal digits. If the zeros look like placeholders, write the answer in scientific notation.
45,678.9 to 3 significant figures is 45,700, best written 4.57 × 10⁴. 999.7 to 3 significant figures carries into a new place: 1,000, written 1.00 × 10³. 0.004876 to 2 significant figures is 0.0049. With the round-half-to-even rule that some lab courses use, 0.125 to 2 significant figures is 0.12 instead of 0.13.
Decimal places vs significant figures
Decimal places count digits after the decimal point; significant figures count from the first non-zero digit. 0.0049 has 4 decimal places but 2 significant figures, and 45,700 has 0 decimal places but 3 significant figures. Use significant figures for measurements and scientific work, and decimal places for money and fixed-precision reports.
This page is for measurement precision: counting, sig fig arithmetic and rounding to a number of significant figures. To round to a place value, a number of decimal places or a multiple, or to compare rounding methods such as banker’s rounding, use the rounding calculator.
Common mistakes with significant figures
- Counting leading zeros: 0.0300 has 3 significant figures, not 5.
- Using the sig fig rule for addition: 18.0 + 1.013 = 19.013 is reported to tenths as 19.0, not as 19.01.
- Letting exact numbers limit the answer: the 2 in 2πr has unlimited significant figures.
- Dropping meaningful zeros: 19.0 and 6.0 × 10⁴ need their zeros to show the precision.
- Rounding every intermediate step instead of once at the end.
Significant figures practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
The leading zeros 0.00 do not count. The 7, the 2 and the trailing zero after the decimal point do, so there are 3.
Both zeros sit between non-zero digits (captive zeros), so all four digits count.
Trailing zeros in a whole number without a decimal point are treated as placeholders, so only 5 and 6 count.
Only the coefficient counts: 2, 0, 4 and the trailing 0 after the decimal point give 4.
Count from the first non-zero digit: 8, 6, 3. The next digit is 4, so the 3 stays: 0.00863.
Keep 7, 9, 9 and look at the 6: round up, which carries to 80,000. Scientific notation, 8.00 × 10^4, shows the 3 significant figures.
The sum is 17.375. Addition keeps the fewest decimal places, and 14.2 has only one, so the answer is 17.4.
3.25 × 0.48 = 1.56. Multiplication keeps the fewest significant figures; 0.48 has 2, so the answer is 1.6.
The 4 is a count, so it is exact. Only 52.6 g limits the answer to 3 significant figures: 210.4 g becomes 210. g (or 2.10 × 10^2 g).
8.45 − 8.41 = 0.04, good to the hundredths, which is only 1 significant figure. Dividing by 2.000 gives 0.02, kept to 1 significant figure.
Quiz complete
Frequently asked questions
How do you calculate significant figures?
Start at the first non-zero digit and count every digit to the right of it, including captive zeros. Count trailing zeros only if the number has a decimal point. For calculations, add and subtract by decimal places, and multiply and divide by significant figures.
How many significant figures does 800 have?
Usually 1, because the two zeros may be placeholders. If all three digits were measured, write 800. or 8.00 × 10², which has 3.
How many significant figures does 1500.00 have?
Six. With a decimal point, every zero after the 15 counts, including the two after the point.
Do significant figures apply to addition?
Not directly. Addition and subtraction round to the fewest decimal places, so 12.11 + 18.0 + 1.013 = 31.1. The number of significant figures in the answer follows from that place.
How do you round to 3 significant figures?
Count three digits from the first non-zero digit and look at the fourth. Round up if it is 5 or more. For example, 0.0045678 becomes 0.00457 and 45,678.9 becomes 45,700, or 4.57 × 10⁴.
How many significant figures should I use?
Use as many as your least precise measurement supports. Your answer cannot be more precise than the data, so a result built from a 2-figure measurement is reported to 2 figures, while exact counts and defined constants do not count against you.
Are exact numbers counted in significant figures?
No. Counted values and defined quantities have unlimited significant figures, so they never reduce the precision of an answer. Put them in square brackets in the calculator, such as [12].
Related calculators
- Rounding calculator: round to places, decimals or multiples with nine rounding methods.
- Scientific notation converter: write answers as a × 10ⁿ.
- Percent error calculator: compare a measured value with the accepted one.
- Logarithm calculator: logs and antilogs with steps.
- Scientific calculator: general calculations before you apply the sig fig rules.
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